Bounds on the minimum distance of additive quantum codes
Bounds on [[89,0]]2
| lower bound: | 21 |
| upper bound: | 31 |
Construction
Construction type: Grassl
Construction of a [[89,0,21]] quantum code:
[1]: [[89, 0, 21]] self-dual quantum code over GF(2^2)
cyclic code of length 89 with generating polynomial x^87 + x^86 + x^83 + x^80 + x^76 + x^75 + x^72 + x^71 + x^69 + x^67 + x^65 + x^64 + x^60 + x^58 + x^56 + x^55 + x^53 + x^51 + x^50 + x^45 + x^44 + x^39 + x^38 + x^36 + x^34 + x^33 + x^31 + x^29 + x^25 + x^24 + x^22 + x^20 + x^18 + x^17 + x^14 + x^13 + x^9 + x^6 + x^3 + x^2 + w
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 1 0 0 1 0 0 1 0 0 1 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 1 1 0 0 1 1 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 1]
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last modified: 2015-06-23
Notes
- All codes establishing the lower bounds where constructed using MAGMA.
- Most upper bounds on qubit codes for n≤100 are based on a MAGMA program by Eric Rains.
- For n>100, the upper bounds on qubit codes are weak (and not necessarily monotone in k).
- Some additional information can be found in the book by Nebe, Rains, and Sloane.
- My apologies to all authors that have contributed codes to this table for not giving specific credits.
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Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024